Would my initial entry in the U.S. as a conditional green card holder be considered illegal if our I-829 application gets denied?

No. Neither your initial entry nor inspection and admission for future adjustment of status purposes will be considered unlawful because of the fraudulent activities of the regional center. Advisably, make sure you always disclose this incident if occasions arise in the future in any immigration processing if the question arises.

No, it would not. It just means the conditional permanent residency may be denied, but your prior status would not be considered unlawful.

Your initial entry as a conditional green card would not be considered "unlawful" nor "not inspected and admitted for future adjustment of status purposes". At that time you were already admitted as a Conditional Permanent Resident.

Your initial entry is a lawful admission to the U.S.

You should not have a problem entering the U.S. That said, the issue would be once you are in the U.S., how to remain in the U.S. and not fall out of status. You need to have the conditions on your conditional green card removed to be able to stay in the U.S. legally. Once your green card expires, if you cannot remove the conditions, without valid immigration status, you could be ordered by immigration enforcement to leave the country.

I would need to know a lot more, but an entry with a valid immigrant visa should be a lawful entry. The circumstances of your continued eligibility may have changed should not affect that, but an I-829 denial would leave you without status.

No. You are admitted, inspected and can change your status if your current conditional green card is denied.

No.

No, the denial of an I-829 does not make your initial entry unlawful. Technically by law even if your I-829 is denied, you continue to be a permanent resident until a Judge orders you removed.

For some purposes, it might not be considered a lawful admission.

No. However, this should be discussed with your investment immigration attorney who can guide you on this and other options you might have.

No, it would not.